Thermal Magnetization Noise and Fluctuation-Dissipation in Magnetoresistive Heads, Sensors, and Ferromagnetic Thin-Film Devices

Continuing technological development of giant magnetoresistive (GMR) spin-valve materials and devices, and tunneling magnetoresistive (TMR) sensors, has been largely driven by ever-increasing demands for greater areal storage density and data transfer rates for hard-disk drives. These technological demands will require future GMR (or TMR) materials with increasing MR coefficients DR/R >> 10%, and read-head/sensor dimensions at and below the scale of 100 nm. In this regime, the sensor's intrinsic electrical noise can be exceeded by resistance noise arising from thermally-induced magnetization fluctuations ("mag-noise") in the very thin, magnetically soft, ferromagnetic sensing layers of the MR read head.

Hence, mag-noise serves as a fundamental limit on GMR sensor signal-to-noise ratio that does not substantially improve with further increases in DR/R or sensitivity c, but which can become more severely limiting as sensor volume decreases.

In addition to its technological implications, observation of mag-noise in sub-micrometer MR sensors provides a relatively simple electrical measurement to study basic damping properties and loss mechanisms in the constituent ultra-thin ferromagnetic films. This can include geometric finite-size effects in very small (100 nm) structures not easily probed by traditional ferromagnetic resonance experiments. The basic relationships between intrinsic magnetic damping and measured thermal magnetization fluctuations can be described by application of the fluctuation-dissipation theorem.

In this talk I will offer a brief tutorial on the fluctuation-dissipation theorem and how it may be properly employed to quantitatively model the mag-noise amplitude and spectrum observed in MR sensors. I will review some recent measurements of mag-noise in MR devices, compare experimental with model expectations, and offer scaling projections of magnetic noise vs. sensor size. In addition, I will discuss how fluctuation-dissipation arguments can discriminate between alternative phenomenological damping models in ways not obvious using traditional uniform magnetization descriptions of damped ferromagnetic resonance, and conclude with a brief consideration of excess damping contributions from inhomogeneity and finite-size effects.